What solid figure has no faces?

Answer 1

All solid figures must have a face. The face need not be planar, but there must be at least one which forms the boundary between the solid and the rest of the universe.

This is somewhat an issue of semantics. A sphere has no edges so some would not say the term face applies to it at all. It does have a surface and you can certainly define that as its face. The point being, it depends on how you define "faces" and it may depend on your context as well.